Question

Shena made a table to show the steps and algebraic properties used to write an equivalent expression for 3x-5+7X+6.

Step
1
2
3
4
Expression3x-5+7x + 6
3x+7X+6-5
(3x+7x)+(6-5)
(3+7)+(6-5)
10x+1
1
Property
Commutative property
Distributive property
Distributive property
Addition property
What error did Shena make?
Shena should have written the associative property for step 1.
Shena should have written the associative property for step 2.
Shena should have written the associative property for step 3.
Shena should have written the associative property for step 4.

Answer 1

Option B is correct

Explanation:

Hope this helps!

Answer 2

2.

Shena should have written the associative property for step 2.

Explanation:

1. Commutative property says
`a+b=b+a.` So, we can use this property to rewrite the expression
`3x-5+7x+6` as
`3x+7x+6-5`

True.

2. Associative property says
`(a+b)+c=a+b+c+a+(b+c).` This means we can put brackets to determine convinient order of operations. Here, in step 2, Shena should use associative property to get

`(3x+7x)+(6-5)`

False.

3. Distributive property that
`(a+b)\cdot c=a\cdot c+b\cdot c.` So,

`(3+7)x+(6-5)`

True

4. Addition property gives that
`3+7=10` and
`6-5=1,` so

`(3+7)x+(6-5)=10x+1`

True.